Question 975043
{{{A*sin^2(theta) + B*cos^2(theta)}}}{{{""=""}}}{{{C}}}

Use the identity {{{cos^2(theta)=1-sin^2(theta)}}}

{{{A*sin^2(theta) + B*(1-sin^2(theta))}}}{{{""=""}}}{{{C}}}

{{{A*sin^2(theta) + B-B*sin^2(theta)}}}{{{""=""}}}{{{C}}}

{{{A*sin^2(theta)-B*sin^2(theta)}}}{{{""=""}}}{{{C-B}}}

{{{sin^2(theta)*(A-B)}}}{{{""=""}}}{{{C-B}}}

{{{sin^2(theta)}}}{{{""=""}}}{{{(C-B)/(A-B)}}}

{{{sin(theta)}}}{{{""=""}}}{{{"" +- sqrt((C-B)/(A-B))}}}

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{{{A*sin^2(theta) + B*cos^2(theta)}}}{{{""=""}}}{{{C}}}

Use the identity {{{sin^2(theta)=1-cos^2(theta)}}}

{{{A*(1-cos^2(theta)) + B*cos^2(theta)}}}{{{""=""}}}{{{C}}}

{{{A-A*cos^2(theta) + B*cos^2(theta)}}}{{{""=""}}}{{{C}}}

{{{-A*cos^2(theta) + B*cos^2(theta)}}}{{{""=""}}}{{{C-A}}}

{{{cos^2(theta)*(-A+B)}}}{{{""=""}}}{{{C-A}}}

{{{cos^2(theta)}}}{{{""=""}}}{{{(C-A)/(-A+B)}}}

{{{cos(theta)}}}{{{""=""}}}{{{"" +- sqrt((C-A)/(-A+B))}}}

{{{cos(theta)}}}{{{""=""}}}{{{"" +- sqrt((C-A)/(B-A))}}}

Edwin</pre>